The law of elastic reflection by a smooth surface is well known: the angle of incidence is equal to the angle of reflection. In contrast, the law of elastic scattering by a rough surface is not unique, but rather depends on the shape of microscopic pits and groves forming the roughness. In the talk a characterization for laws of scattering by rough surfaces will be given. We will also consider some problems of optimal resistance for rough bodies which can be naturally interpreted in terms of optimal roughening of artificial satellites’ surface on low Earth orbits. We will show that these problems can be reduced to optimal mass transportation (OMT) on the sphere with quadratic cost, and then solve a special OMT problem of this kind.